"Then there exists a homogeneous function $\rho\in C^\infty(R^n \backslash\{0\},R^n)$ with negative degree of homogeneity which specifies the following properties:" - Pablo Monzon (2006), Almost global stability of dynamical systems, page 27., Link to the e-book
Does backslash have a meaning in this context in math. According to Wolfram Mathworld it can sometimes have meaning. But, does it have one here?
Yes, it has a common meaning. In general for two sets $A$ and $B$, $$ A\backslash B \equiv A\text{ without } B $$ so in your case, $\mathbb{R}^n\backslash\{0\}$ means $\mathbb{R}^n$ without the origin $0$ or $$ \mathbb{R}^n\backslash\{0\}\equiv\{x\in\mathbb{R}^n:||x||>0\} $$ As Daan Michiels points out, the notation of set difference does sometimes vary, for example $$ \mathbb{R}^n - \{0\}\equiv\mathbb{R}^n\backslash\{0\} $$ is also used to express this. You might also have a look here.